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Integrate the functions (e^(x))/((1+e^...

Integrate the functions
`(e^(x))/((1+e^(x))(2+e^(x)))`

Text Solution

Verified by Experts

The correct Answer is:
`log|1+e^(x)|-log|2+e^(x)|+c`
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KUMAR PRAKASHAN-INTEGRALS -MISCELLANEOUS EXERCISE-7
  1. Find the integrals of the functions 1/(cos(x – a) cos (x – b))

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  2. Integrate the functions (x^(3))/(sqrt(1-x^(8)))

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  3. Integrate the functions (e^(x))/((1+e^(x))(2+e^(x)))

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  4. Integrate the function is Exercise. (1)/((x^(2)+1)(x^(2)+4))

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  5. Integrate the function is Exercise. cos^(3)x e^(log sinx)

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  6. Integrate the functions e^(3logx)(x^(4)+1)^(-1)

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  7. Integrate the functions f'(ax+b)[f(ax+b)]^(n)

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  8. Integrate the function is. (1)/(sqrt(sin^(3)x sin(x+alpha)))

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  9. Integrate the function is Exercise. (sin^(-1) sqrt(x)-cos^(-1)sqrt(x...

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  10. Integrate the function is Exercise. sqrt((1-sqrt(x))/(1+sqrt(x)))

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  11. Integrate the functions (2+sin2x)/(1+cos2x)e^(x)

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  12. Integrate the function is Exercise. (x^(2)+x+1)/((x+1)^(2)+(x+2))

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  13. Integrate the functions tan^(-1)sqrt((1-x)/(1+x))

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  14. Integrate the function is (xcos^-1x)/sqrt(1-x^2)

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  15. Evaluate the definite integrals int(pi/2)^(pi)e^(x)((1-sinx)/(1-cosx...

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  16. Evaluate the definite integrals int(0)^(pi/4)(sinxcosx)/(cos^(4)x+si...

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  17. Evaluate the definite integrals in exercise. overset((pi)/(2)) under...

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  18. Evaluate the definite integrals in exercise. overset((pi)/(3)) under...

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  19. Evaluate the definite integrals int(0)^(1)(dx)/(sqrt(1+x)-sqrtx)

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  20. Evaluate the definite integrals int(0)^(pi/4)(sinx+cosx)/(9+16sin2x)...

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